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Scott, MIT Graduate

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Themistocle Qin discovers a metal sphere of unusual

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Themistocle Qin discovers a metal sphere of unusual properties this Bensalemite sphere has a radius of 80.00 cm and density of 1.753g/cm 3 at 300.00K and atmospheric pressure. Further investigations reveal that Bensalemite transfers heat almost instantaneously, has a large coefficient of thermal expansion (x=3.071 x 10-2/C 0), and is elastic but rather incompressible (bulk modulus 9737GPa). Qin uses cold and pressure to compress the Bensalemite sphere. When the sphere is compressed under a pressure of 2001.0403 atmospheres and cooled to the boiling point of liquid nitrogen (-195.79o C) find the following for the Bensalemite sphere. A. Volume B. Density C. Speed of sound. This is for highschool Physic, thank you, deborah

Yes, the coefficient of thermal expansion is usually assigned the variable name "alpha", which is a Greek letter "a".

But it's the values rather than the variable names that are a problem here.

Does this equation look familiar:

∆V = 3V(alpha)∆T

That is the usual formula for the change in volume. Perhaps your course is teaching something different.

The most suspicious number is ***** value of alpha. Most coefficients of thermal expansion are in the range of 1 x 10^-6 to 200 x 10^-6, so a value of 3.071 x 10^-2 is HUGE.

I have no idea what your teacher may be trying to do. But I have seen a variety of teachers teach unusual things, so there is always the possibility that I'm just not familiar with the particular approach that you are being taught.

What textbook are you using? Perhaps I can find it online.

Ryan, The teacher isn't changing anything and I've double proofed my question. Should I submit your answer anyway? What about the other two answers needed?

The difficulty is that the three answers depend on each other. You need the answer to the volume question to calculate the new density for part 2, and then you need that new density to calculate the speed of sound in part 3.

It would be one thing if we were coming up with a volume that was just unusual, like a 95% change in volume. But the result that we are getting is an impossible result. The volume cannot be negative, so the minimum volume would have to be 0, which would make the density infinite (since you can't divide by 0), and then the speed of sound would be 0, since you would be dividing the bulk modulus by an infinite density.

In essence, this process would be creating a black hole. Perhaps that is what your instructor is leading you toward, even though that seems a bit silly. (Does he seem like the sort that would give you a "trick" question like this?)

I can write up a solution that way if you'd like. Alternatively, if you can send me some of the equations from the section of your textbook where this kind of topic is covered, perhaps I can figure out what they are thinking.